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<h1>Wisconsin Computer Vision Group Publications</h1>
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Click on any of the following topics to jump to that set of papers
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<DD><!WA0><!WA0><!WA0><img alg="o" src="http://www.cs.wisc.edu/~dyer/images/redball.gif">
    <!WA1><!WA1><!WA1><A HREF="#exploration">Visual Exploration</A>
<DD><!WA2><!WA2><!WA2><img alg="o" src="http://www.cs.wisc.edu/~dyer/images/redball.gif">
    <!WA3><!WA3><!WA3><A HREF="#motion">Motion Analysis</A>
<DD><!WA4><!WA4><!WA4><img alg="o" src="http://www.cs.wisc.edu/~dyer/images/redball.gif">
    <!WA5><!WA5><!WA5><A HREF="#shape">3D Shape Representation</A>
<DD><!WA6><!WA6><!WA6><img alg="o" src="http://www.cs.wisc.edu/~dyer/images/redball.gif">
    <!WA7><!WA7><!WA7><A HREF="#snakes">Deformable Contours</A>
<DD><!WA8><!WA8><!WA8><img alg="o" src="http://www.cs.wisc.edu/~dyer/images/redball.gif">
    <!WA9><!WA9><!WA9><A HREF="#visualization">Visualization</A>
<P>

<HR>
<!WA10><!WA10><!WA10><A HREF="http://www.cs.wisc.edu/computer-vision/">
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<P>
<H2><A NAME="exploration">Visual Exploration</A></H2>
<UL>
<LI><!WA12><!WA12><!WA12><img alg="o" src="http://www.cs.wisc.edu/~dyer/images/new.gif">
    <B><A NAME="fest96-yu">Shape Recovery from Stationary Surface Contours by Controlled Observer Motion</A></B><BR>
     L. Yu and C. R. Dyer,
     in <CITE>Advances in Image Understanding: A Festschrift for Azriel Rosenfeld</CITE>, IEEE Computer Society Press, Los Alamitos, Ca., 1996, 177-193.
     (<!WA13><!WA13><!WA13><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/fest96-yu.ps">960K postscript</A>)
<p>
<blockquote>
The projected deformation of stationary contours and markings on
object surfaces is analyzed in this paper. It is shown that given a
marked point on a stationary contour, an active observer can move
deterministically to the osculating plane for that point by observing
and controlling the deformation of the projected contour. Reaching the
osculating plane enables the observer to recover the object surface
shape along the contour as well as the Frenet frame of the
contour. Complete local surface recovery requires either two
intersecting surface contours and the knowledge of one principle
direction, or more than two intersecting contours. To reach the
osculating plane, two strategies involving both pure translation and a
combination of translation and rotation are analyzed. Once the Frenet
frame for the marked point on the contour is recovered, the same
information for all points on the contour can be recovered by staying
on osculating planes while moving along the contour. It is also shown
that occluding contours and stationary contours deform in a
qualitatively different way and the problem of discriminating between
these two types of contours can be resolved before the recovery of
local surface shape.
</blockquote>


<LI>
    <B><A NAME="ijcv94-kutulakos">Recovering Shape by Purposive Viewpoint Adjustment</A></B><BR>
     K. N. Kutulakos and C. R. Dyer,
     <CITE>Int. J. Computer Vision</CITE> <B>12</B>, 1994, 113-136.  
    (<!WA14><!WA14><!WA14><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/ijcv94-kutulakos.ps">postscript</A>
    or <!WA15><!WA15><!WA15><A NAME="ijcv94-kutulakos" HREF="ftp://ftp.cs.wisc.edu/computer-vision/ijcv94-kutulakos.ps.gz">570K gzip'ed postscript</A>)<br>
     (Earlier versions appeared in
     <CITE>Proc. Computer Vision and Pattern Recognition Conf.</CITE>,
     1992, 16-22  
     (<!WA16><!WA16><!WA16><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/cvpr92-kutulakos.ps">postscript</A>
     or <!WA17><!WA17><!WA17><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/cvpr92-kutulakos.ps.gz">90K gzip'ed postscript</A>),<BR>
     and as Computer Sciences Department
     <CITE>Technical Report 1035</CITE> 
     (<!WA18><!WA18><!WA18><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/tr1035-kutulakos.ps">postscript</A>
     or <!WA19><!WA19><!WA19><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/tr1035-kutulakos.ps.gz">160K gzip'ed postscript</A>).) 
<p> 
<blockquote>
  We present an approach for recovering surface shape from the occluding
  contour using an active (i.e., moving) observer.  It is based on a relation
  between the geometries of a surface in a scene and its occluding contour: If
  the viewing direction of the observer is along a principal direction for a
  surface point whose projection is on the contour, surface shape (i.e.,
  curvature) at the surface point can be recovered from the contour. Unlike
  previous approaches for recovering shape from the occluding contour, we use
  an observer that <EM>purposefully</EM> changes viewpoint in order to
  achieve a
  well-defined geometric relationship with respect to a 3D shape prior to its
  recognition.  We show that there is a simple and efficient viewing strategy
  that allows the observer to align the viewing direction with one of the two
  principal directions for a point on the surface. This strategy depends on
  only curvature measurements on the occluding contour and therefore
  demonstrates that recovering quantitative shape information from the contour
  does not require knowledge of the velocities or accelerations of the
  observer.  Experimental results demonstrate that our method can be easily
  implemented and can provide reliable shape information from the occluding
  contour.
</blockquote>


<LI> <B><A NAME="cvpr94-1-kutulakos">
     Occluding Contour Detection using Affine Invariants and Purposive
     Viewpoint Control</A></B><BR>
     K. N. Kutulakos and C. R. Dyer,
     <CITE>Proc. Computer Vision and Pattern Recognition Conf.</CITE>,
     1994, 323-330.  
     (Received Siemens Best Paper Award <!WA20><!WA20><!WA20><img alg="o" src="http://www.cs.wisc.edu/~dyer/images/award.gif">) 
     (<!WA21><!WA21><!WA21><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/cvpr94-1-kutulakos.ps">postscript</A>
     or <!WA22><!WA22><!WA22><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/cvpr94-1-kutulakos.ps.gz">190K gzip'ed postscript</A>)<P>
<blockquote>
  We present an approach for identifying the occluding contour and
  determining its sidedness using an active (i.e., moving) observer.
  It is based on the <EM>non-stationarity property</EM> of the visible
  rim: When the observer's viewpoint is changed, the visible rim is a
  collection of curves that ``slide,'' rigidly or non-rigidly, over
  the surface.  We show that the observer can deterministically choose
  three views on the tangent plane of selected surface points to
  distinguish such curves from stationary surface curves (i.e.,
  surface markings). Our approach demonstrates that the occluding
  contour can be identified <EM> directly</EM>, i.e., without first
  computing surface shape (distance and curvature).
</blockquote>


<LI> <B><A NAME="cvpr94-2-kutulakos">
     Global Surface Reconstruction by Purposive Control of Observer Motion</A></B><BR>
     K. N. Kutulakos and C. R. Dyer,
     <CITE>Artificial Intelligence</CITE> <B>78</B>, No. 1-2, 1995, 147-177.
     (<!WA23><!WA23><!WA23><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/aij95-kutulakos.tar.gz">2.0M gzip'ed tar file</A>)
     <BR>
     (Earlier version appeared in
     <CITE>Proc. Computer Vision and Pattern Recognition Conf.</CITE>,
     1994, 331-338.
     (<!WA24><!WA24><!WA24><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/cvpr94-2-kutulakos.ps">postscript</A>
     or <!WA25><!WA25><!WA25><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/cvpr94-2-kutulakos.ps.gz">370K gzip'ed postscript</A>).)<BR>
     (Longer version appears as Computer Sciences Department
     <CITE>Technical Report 1141</CITE>
     (<!WA26><!WA26><!WA26><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/tr1141-kutulakos.ps">postscript</A>
     or <!WA27><!WA27><!WA27><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/tr1141-kutulakos.ps.gz">1.1M gzip'ed postscript</A>).) <P>
<blockquote>
What viewpoint-control strategies are important for performing global
visual exploration tasks such as searching for specific surface
markings, building a global model of an arbitrary object, or
recognizing an object?  In this paper we consider the task of
purposefully controlling the motion of an active, monocular observer
in order to recover a global description of a smooth,
arbitrarily-shaped object.  We formulate global surface reconstruction
as the task of controlling the motion of the observer so that the
visible rim slides over the maximal, connected, reconstructible
surface regions intersecting the visible rim at the initial
viewpoint. We show that these regions are bounded by a subset of the
visual event curves defined on the surface.
<P>
By studying the epipolar parameterization, we develop two basic
strategies that allow reconstruction of a surface region around any
point in a reconstructible surface region.  These strategies control
viewpoint to achieve and maintain a well-defined geometric
relationship with the object's surface, rely only on information
extracted directly from images (e.g., tangents to the occluding
contour), and are simple enough to be performed in real time. We
then show how global surface reconstruction can be provably achieved
by (1) appropriately integrating these strategies to iteratively
``grow'' the reconstructed regions, and (2) obeying four simple
rules.
</blockquote>

<LI> <B><A NAME="cbvw94-kutulakos">
     Building Global Object Models by Purposive Viewpoint Control</A></B><BR>
     K. N. Kutulakos, W. B. Seales, and C. R. Dyer,
     <CITE>Proc. 2nd CAD-Based Vision Workshop</CITE>,
     1994, 169-182.
     (<!WA28><!WA28><!WA28><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/cbvw94-kutulakos.ps">postscript</A>
     or <!WA29><!WA29><!WA29><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/cbvw94-kutulakos.ps.gz">760K gzip'ed postscript</A>)<BR>
     (An earlier version appeared in
     <CITE>Proc. SPIE: Sensor Fusion VI</CITE>, 
     1993, 368-383
     (<!WA30><!WA30><!WA30><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/spie93-kutulakos.ps">postscript</A>
     or <!WA31><!WA31><!WA31><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/spie93-kutulakos.ps.gz">740K gzip'ed postscript</A>).)<P>
<blockquote>
We present an approach for recovering a global surface model of an
object from the deformation of the occluding contour using an active
(i.e., mobile) observer able to control its motion. In particular, we
consider two problems: (1) How can the observer's viewpoint be
controlled in order to generate a dense sequence of images that allows
incremental reconstruction of an unknown surface, and (2) how can we
construct a global surface model from the generated image sequence?
Solving these two problems is crucial for automatically constructing
models of objects whose surface is non-convex and self-occludes. We
achieve the first goal by <EM>purposefully</EM> and <EM>qualitatively</EM>
controlling the observer's instantaneous direction of motion in order
to control the motion of the visible rim over the surface.  We achieve
the second goal by using a calibrated trinocular camera rig and a
mechanism for controlling the relative position and orientation of the
viewed surface with respect to the trinocular rig.
</blockquote>

<LI> <B><A NAME="thesis-kutulakos">
     Exploring Three-Dimensional Objects by Controlling the Point of
     Observation</A></B><BR>
     K. N. Kutulakos, Ph.D. Dissertation,
     Computer Sciences Department Technical Report 1251,
     University of Wisconsin - Madison, October 1994.
     (<!WA32><!WA32><!WA32><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/thesis-kutulakos.ps">postscript</A>
     or <!WA33><!WA33><!WA33><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/thesis-kutulakos.zip">5.1M zip-compressed postscript</A>)<P>
<blockquote>
In this thesis we study how controlled movements of a camera can be
used to infer properties of a curved object's three-dimensional shape.
The unknown geometry of an environment's objects, the effects of
self-occlusion, the depth ambiguities caused by the projection
process, and the presence of noise in image measurements are a few of
the complications that make object-dependent movements of the camera
advantageous in certain shape recovery tasks.  Such movements can
simplify local shape computations such as curvature estimation, allow
use of weaker camera calibration assumptions, and enable the
extraction of global shape information for objects with complex
surface geometry.  The utility of object-dependent camera movements is
studied in the context of three tasks, each involving the extraction
of progressively richer information about an object's unknown shape:
(1) detecting the occluding contour, (2) estimating surface curvature
for points projecting to the contour, and (3) building a
three-dimensional model for an object's entire surface.  Our main
result is the development of three distinct active vision strategies
that solve these three tasks by controlling the motion of a camera.
<P>

Occluding contour detection and surface curvature estimation are
achieved by exploiting the concept of a special viewpoint: For
any image there exist special camera positions from which the object's
view trivializes these tasks.  We show that these positions can be
deterministically reached, and that they enable shape recovery even
when few or no markings and discontinuities exist on the object's
surface, and when differential camera motion measurements cannot be
accurately obtained.
<P>

A basic issue in building three-dimensional global object models is
how to control the camera's motion so that previously-unreconstructed
regions of the object become reconstructed.  A fundamental difficulty
is that the set of reconstructed points can change unpredictably
(e.g., due to self-occlusions) when ad hoc motion strategies are
used.  We show how global model-building can be achieved for generic
objects of arbitrary shape by controlling the camera's motion on
automatically-selected surface tangent and normal planes so that the
boundary of the already-reconstructed regions is guaranteed to
"slide" over the object's entire surface.
<P>

Our work emphasizes the need for (1) controlling camera motion
through efficient processing of the image stream, and (2) designing
provably-correct strategies, i.e., strategies whose success can be
accurately characterized in terms of the geometry of the viewed
object.  For each task, efficiency is achieved by extracting from
each image only the information necessary to move the camera
differentially, assuming a dense sequence of images, and using 2D
rather than 3D information to control camera motion.  Provable
correctness is achieved by controlling camera motion based on the
occluding contour's dynamic shape and maintaining specific
task-dependent geometric constraints that relate the camera's motion
to the differential geometry of the object.
</blockquote>

<LI> <B><A NAME="cvpr93-kutulakos">
     Toward Global Surface Reconstruction by Purposive 
     Viewpoint Adjustment</A></B><br>
     K. N. Kutulakos and C. R. Dyer, 
     <CITE> Proc. Computer Vision and Pattern 
     Recognition Conf.</CITE>, 1993, 726-727.
     (<!WA34><!WA34><!WA34><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/cvpr93-kutulakos.ps">postscript</A>
     or <!WA35><!WA35><!WA35><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/cvpr93-kutulakos.ps.gz">10K gzip'ed postscript</A>)<P>
<blockquote>
We consider the following problem: How should an observer change viewpoint
in order to generate a dense image sequence of an arbitrary smooth surface
so that it can be incrementally reconstructed using the occluding contour
and the epipolar parameterization?  We present a collection of qualitative
behaviors that, when integrated appropriately, purposefully control
viewpoint based on the appearance of the surface in order to provably solve
this problem.
</blockquote>

<LI> <B><A NAME="tr1124-kutulakos">
     Object Exploration By Purposive, Dynamic Viewpoint 
     Adjustment</A></B><br>
     K. N. Kutulakos, C. R. Dyer, V. J. Lumelsky, 
     Computer Sciences Department Technical Report 1124,
     November 1992.
     (<!WA36><!WA36><!WA36><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/tr1124-kutulakos.ps">postscript</A>
     or <!WA37><!WA37><!WA37><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/tr1124-kutulakos.ps.gz">110K gzip'ed postscript</A>)<P>
<blockquote>
  We present a viewing strategy for exploring the surface of an unknown
  object (i.e., making all of its points visible) by purposefully
  controlling the motion of an active observer. It is based on a simple
  relation between (1) the instantaneous direction of motion of the
  observer, (2) the visibility of points projecting to the occluding
  contour, and (3) the surface normal at those points: If the dot product of
  the surface normal at such points and the observer's velocity is positive,
  the visibility of the points is guaranteed under an infinitesimal
  viewpoint change. We show that this leads to an object exploration
  strategy in which the observer <EM>purposefully</EM> controls its motion
  based on the occluding contour in order to impose structure on the set of
  surface points explored, make its representation simple and qualitative,
  and provably solve the exploration problem for smooth generic surfaces of
  arbitrary shape. Unlike previous approaches where exploration is cast as a
  discrete process (i.e., asking where to look next?) and where the
  successful exploration of arbitrary objects is not guaranteed, our
  approach demonstrates that dynamic viewpoint control through directed
  observer motion leads to a qualitative exploration strategy that is
  provably-correct, depends only on the dynamic appearance of the
  occluding contour, and does not require the recovery of detailed
  three-dimensional shape descriptions from every position of the observer.
</blockquote>


<LI> <B><A NAME="icra94-kutulakos">
     Provable Strategies for Vision-Guided Exploration in Three Dimensions</A></B><BR>
     K. N. Kutulakos, C. R. Dyer, and V. J. Lumelsky,
     <CITE>Proc. 1994 IEEE Int. Conf. Robotics and Automation</CITE>,
     1994, 1365-1372.
     (<!WA38><!WA38><!WA38><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/icra94-kutulakos.ps">postscript</A>
     or <!WA39><!WA39><!WA39><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/icra94-kutulakos.ps.gz">210K gzip'ed postscript</A>)<P>
<blockquote>
An approach is presented for exploring an unknown, arbitrary surface
in three-dimensional (3D) space by a mobile robot.  The main
contributions are (1) an analysis of the capabilities a robot must
possess and the trade-offs involved in the design of an exploration
strategy, and (2) two provably-correct exploration strategies that
exploit these trade-offs and use visual sensors (e.g., cameras and
range sensors) to plan the robot's motion.  No such analysis existed
previously for the case of a robot moving freely in 3D space.  The
approach exploits the notion of the <EM>occlusion boundary</EM>, i.e.,
the points separating the visible from the occluded parts of an
object.  The occlusion boundary is a collection of curves that
``slide'' over the surface when the robot's position is continuously
controlled, inducing the visibility of surface points over which they
slide.  The paths generated by our strategies force the occlusion
boundary to slide over the entire surface.  The strategies provide a
basis for integrating motion planning and visual sensing under a
common computational framework.
</blockquote>

<LI> <B><A NAME="icra93-kutulakos">
     Vision-Guided Exploration:  A Step toward General Motion
     Planning in Three Dimensions</A></B><br>
     K. N. Kutulakos, 
     V. J. Lumelsky, and C. R. Dyer, <CITE> Proc. 1993 IEEE 
     Int. Conf. on Robotics and Automation</CITE>, 1993, 289-296. 
     (<!WA40><!WA40><!WA40><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/icra93-kutulakos.ps">postscript</A>
     or <!WA41><!WA41><!WA41><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/icra93-kutulakos.ps.gz">50K gzip'ed postscript</A>)<BR>
     (Longer version appears as Computer Sciences Department
     <CITE>Technical Report 1111</CITE>
     (<!WA42><!WA42><!WA42><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/tr1111-kutulakos.ps">postscript</A>
     or <!WA43><!WA43><!WA43><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/tr1111-kutulakos.ps.gz">90K gzip'ed postscript</A>).)<P>
<blockquote>
We present an approach for solving the path planning problem for a mobile
robot operating in an unknown, three dimensional environment containing
obstacles of arbitrary shape.  The main contributions of this paper are (1)
an analysis of the type of sensing information that is necessary and
sufficient for solving the path planning problem in such environments, and
(2) the development of a framework for designing a provably-correct
algorithm to solve this problem.  Working from first principles, without any
assumptions about the environment of the robot or its sensing capabilities,
our analysis shows that the ability to explore the obstacle surfaces (i.e.,
to make all their points visible) is intrinsically linked with the ability
to plan the motion of the robot.  We argue that current approaches to the
path planning problem with incomplete information simply do not extend to
the general three-dimensional case, and that qualitatively different
algorithms are needed.
</blockquote>



</UL>
<HR>
<P>
<H2><A NAME="motion">Motion Analysis</A></H2>
<UL>

<LI><B><A NAME="iccv95-seitz">
     Complete Scene Structure from Four Point Correspondences</A></B><BR>
     S. M. Seitz and C. R. Dyer,
     <CITE>Proc. 5th Int. Conf. Computer Vision</CITE>,
     1995, 330-337.
     (<!WA44><!WA44><!WA44><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/iccv95-seitz.ps">postscript</A>
     or <!WA45><!WA45><!WA45><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/iccv95-seitz.ps.gz">250K gzip'ed postscript</A>)<P>
<blockquote>
A new technique is presented for computing 3D scene structure from point 
and line features in monocular image sequences.  Unlike previous methods, 
the technique guarantees the completeness of the recovered scene, ensuring 
that every scene feature that is detected in each image is reconstructed.
The approach relies on the presence of four or more reference features 
whose correspondences are known in all the images.  Under an orthographic 
or affine camera model, the parallax of the reference features provides 
constraints that simplify the recovery of the rest of the visible scene.
An efficient recursive algorithm is described that uses a unified framework 
for point and line features.  The algorithm integrates the tasks of feature 
correspondence and structure recovery, ensuring that all reconstructible 
features are tracked.  In addition, the algorithm is immune to outliers and
feature-drift, two weaknesses of existing structure-from-motion techniques.
Experimental results are presented for real images.
</blockquote>

<LI> <B><A NAME="nram94-seitz">
     Detecting Irregularities in Cyclic Motion</A></B><BR>
     S. M. Seitz and C. R. Dyer,
     <CITE>Proc. Workshop on Motion of Non-Rigid and Articulated Objects</CITE>,
     1994, 178-185.
     (<!WA46><!WA46><!WA46><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/nram94-seitz.ps">postscript</A>
     or <!WA47><!WA47><!WA47><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/nram94-seitz.ps.gz">910K gzip'ed postscript</A>)<P>
<blockquote>
Real cyclic motions tend not to be perfectly even, i.e., the period varies 
slightly from one cycle to the next, because of physically important changes
in the scene.  A generalization of period is defined for cyclic motions
that makes periodic variation explicit.  This representation, called the 
period trace, is compact and purely temporal, describing the evolution 
of an object or scene without reference to spatial quantities such as 
position or velocity.  By delimiting cycles and identifying correspondences 
across cycles, the period trace provides a means of temporally registering 
a cyclic motion.  In addition, several purely temporal motion features are 
derived, relating to the nature and location of irregularities.  Results 
are presented using real image sequences and applications to athletic and 
medical motion analysis are discussed.
</blockquote>


<LI> <B><A NAME="cvpr94-seitz">
     Affine Invariant Detection of Periodic Motion</A></B><BR>
     S. M. Seitz and C. R. Dyer,
     <CITE>Proc. Computer Vision and Pattern Recognition Conf.</CITE>,
     1994, 970-975.
     (<!WA48><!WA48><!WA48><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/cvpr94-seitz.ps">postscript</A>
     or <!WA49><!WA49><!WA49><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/cvpr94-seitz.ps.gz">1M gzip'ed postscript</A>)<BR>
     (Different version appears as Computer Sciences Department
     <CITE>Technical Report 1225</CITE>
     (<!WA50><!WA50><!WA50><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/tr1225-seitz.ps">postscript</A>
     or <!WA51><!WA51><!WA51><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/tr1225-seitz.ps">890K gzip'ed postscript</A>).)<P>
<blockquote>
Current approaches for detecting periodic motion assume a stationary camera
and place limits on an object's motion.  These approaches rely on the
assumption that a periodic motion projects to a set of periodic image
curves, an assumption that is invalid in general.
Using affine-invariance,  we
derive necessary and sufficient conditions for an image sequence to be
the projection of a periodic motion.  No restrictions are placed on
either the motion of the camera or the object.
Our algorithm is shown to be provably-correct for
noise-free data and is extended to be robust with respect to
occlusions and noise.  The extended algorithm is evaluated with real and
synthetic image sequences.
</blockquote>


<LI> <B><A NAME="cvgip93-allmen">
     Computing Spatiotemporal Relations for Dynamic Perceptual
     Organization</A></B><BR>
     M. Allmen and C. R. Dyer,
     <CITE>Computer Vision, Graphics and Image Processing:  Image
     Understanding</CITE><B> 58</B>, 1993, 338-351.
     (<!WA52><!WA52><!WA52><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/cvgip93-allmen.ps">postscript</A>
     or <!WA53><!WA53><!WA53><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/cvgip93-allmen.ps.gz">200K gzip'ed postscript</A>)<BR>
     (Earlier version appeared
     as Computer Sciences Department
     <CITE>Technical Report 1130</CITE>
     (<!WA54><!WA54><!WA54><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/tr1130-allmen.ps">postscript</A>
     or <!WA55><!WA55><!WA55><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/tr1130-allmen.ps.gz">200K gzip'ed postscript</A>).) 
     <P>
<blockquote>
To date, the overwhelming use of motion in computational vision has been
to recover the three-dimensional structure of the
scene. We propose that there are other, more powerful, uses for motion.
Toward this end,
we define dynamic perceptual organization as an extension
of the traditional (static) perceptual organization approach.
Just as
static perceptual organization groups coherent features in an image,
dynamic perceptual organization groups coherent motions through an image
sequence. Using dynamic perceptual organization, we propose a new paradigm
for motion understanding and show why it can be
done independently of the recovery of scene structure and scene motion.
The paradigm starts with a spatiotemporal cube of image data and organizes
the paths of points so that
interactions between the paths and perceptual
motions such as common, relative and cyclic
are made explicit.
The results of this can then be used for high-level motion recognition tasks.
</blockquote>


<LI> <B><A NAME="qv93-waldon">
     Dynamic Shading, Motion Parallax and Qualitative Shape</A></B><BR>
     S. Waldon and C. R. Dyer, <CITE>Proc. IEEE 
     Workshop on Qualitative Vision</CITE>, 1993, 61-70.
     (<!WA56><!WA56><!WA56><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/qv93-waldon.ps">postscript</A>
     or <!WA57><!WA57><!WA57><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/qv93-waldon.ps.gz">140K gzip'ed postscript</A>)<P>
<blockquote>
We address the problem of qualitative shape
recovery from moving surfaces. Our analysis is unique in that we
consider specular interreflections and explore the effects of both
motion parallax and changes in shading. To study this situation we
define an image flow field called the reflection flow field,
which describes the motion of reflection points and the motion of the
surface. From a kinematic analysis, we show that the reflection flow
is qualitatively different from the motion parallax because it is
discontinuous at or near parabolic curves. We also show that when the
gradient of the reflected image is strong, gradient-based flow
measurement techniques approximate the reflection flow field and not
the motion parallax. We conclude from these analyses that reliable
qualitative shape information is generally available only at
discontinuities in the image flow field.
</blockquote>


<LI> <B><A NAME="thesis-allmen">
     Image Sequence Description using Spatiotemporal Flow Curves:
     Toward Motion-Based Recognition</A></B><BR>
     Ph.D. Dissertation, M. C. Allmen,
     Computer Sciences Department Technical Report 1040,
     August 1991.
     (<!WA58><!WA58><!WA58><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/thesis-allmen.ps">postscript</A>
     or <!WA59><!WA59><!WA59><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/thesis-allmen.ps.gz">1.1M gzip'ed postscript</A>)<P>
<blockquote>
Recovering a hierarchical motion description of a long image sequence is
one way to recognize objects and their motions.
Intermediate-level and high-level motion analysis, i.e., recognizing a
coordinated sequence of events
such as walking and throwing,
has been formulated previously as a process that follows high-level object
recognition. This thesis develops an alternative approach to
intermediate-level and high-level motion analysis.
It does not depend on complex object descriptions and can therefore be
computed prior to object recognition. Toward this end,
a new computational framework for low and intermediate-level processing of
long sequences of images is
presented.
<P>
 
Our new computational framework
uses spatiotemporal (ST) surface flow and ST flow curves.
As contours move, their projections
into the image also move. Over time, these projections sweep out
ST surfaces. Thus, these
surfaces are direct representations of object motion.
ST surface flow is defined as the natural extension
of optical flow to
ST surfaces. For every point on an ST surface, the instantaneous
velocity of that point on the surface is recovered.
It is observed that arc length of a rigid contour does not change if
that contour is moved in the direction of motion on the ST surface. Motivated
by this observation, a function measuring arc length change is defined.
The direction of motion of a contour undergoing
motion parallel to the image plane is shown to be perpendicular to the
gradient of this function.
<P>
 
ST surface flow is then used to recover ST flow curves. ST flow curves
are defined such that the tangent at a point on the curve equals the ST
surface flow at that point. ST flow curves are then grouped so that each
cluster represents a temporally-coherent structure, i.e.,
structures that result
from an object or surface in the scene undergoing motion. Using these clusters
of ST flow curves, separate moving objects in the scene can be hypothesized
and occlusion and disocclusion between them can be identified.
<P>
 
The problem of detecting cyclic motion, while recognized by the psychology
community, has received very little attention in the computer vision
community. In order to show the representational
power of ST flow curves, cyclic motion is detected using ST flow curves
without prior recovery of complex object descriptions.
</blockquote>


</UL>
<HR>
<P>
<H2><A NAME="shape">3D Shape Representation</A></H2>
<UL>

<LI><!WA60><!WA60><!WA60><img alg="o" src="http://www.cs.wisc.edu/~dyer/images/new.gif"> 
     <B><A NAME="sigg96-seitz"> View Morphing</A></B><BR>
     S. M. Seitz and C. R. Dyer, <CITE>Proc. SIGGRAPH 96</CITE>, 1996, To
     appear. 
(<!WA61><!WA61><!WA61><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/sigg96-seitz.ps">
4.2M postscript</A>
or <!WA62><!WA62><!WA62><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/sigg96-seitz.ps.gz">
1.6M gzip'ed postscript</A>)<P>
<blockquote>
Image morphing techniques can generate compelling 2D transitions between
images.  However, differences in object pose or viewpoint often cause
unnatural distortions in image morphs that are difficult to correct
manually.  Using basic principles of projective
geometry, this paper introduces a simple extension to image morphing
that correctly handles 3D projective camera and scene transformations.
The technique, called <I> view morphing</I>, works by prewarping two images
prior to computing a morph and then postwarping the interpolated images.
Because no knowledge of 3D shape is required, the technique may be applied
to photographs and drawings, as well as rendered scenes.
The ability to synthesize changes both in viewpoint and image structure
affords a wide variety of interesting 3D effects via simple image
transformations.
</blockquote>

<LI><!WA63><!WA63><!WA63><img alg="o" src="http://www.cs.wisc.edu/~dyer/images/new.gif"> 
     <B><A NAME="icpr96-seitz"> Toward Image-Based Scene Representation
	  Using View Morphing</A></B><BR>
     S. M. Seitz and C. R. Dyer, <CITE>Proc. 13th Int. Conf. Pattern
	  Recognition, Vol. I, Track A: Computer Vision</CITE>, 1996, 84-89.
(<!WA64><!WA64><!WA64><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/icpr96-seitz.ps">
1.2M postscript</A>
or <!WA65><!WA65><!WA65><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/icpr96-seitz.ps.gz">
486K gzip'ed postscript</A>)
     (Longer version appears as Computer Sciences Department
     <CITE>Technical Report 1298</CITE>
     (<!WA66><!WA66><!WA66><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/tr1298-seitz.ps">postscript</A>
     or <!WA67><!WA67><!WA67><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/tr1298-seitz.ps">552K gzip'ed postscript</A>).)<P>
<blockquote>
The question of which views may be inferred from a set of basis images
is addressed.  Under certain conditions, a discrete set of images
implicitly describes scene appearance for a continuous range of viewpoints.
In particular, it is demonstrated that two basis views of a static scene
determine the set of all views on the line between their optical centers.
Additional basis views further extend the range of predictable views to a
two- or three-dimensional region of viewspace.  These results are shown to
apply under perspective projection subject to a generic visibility
constraint called monotonicity.  In addition, a simple scanline algorithm is
presented for actually generating these views from a set of basis images.
The technique, called <I> view morphing</I> may be applied to both calibrated
and uncalibrated images.  At a minimum, two basis views and their
fundamental matrix are needed.  Experimental results are presented on
real images.  This work provides a theoretical foundation for image-based
representations of 3D scenes by demonstrating that perspective view
synthesis is a theoretically well-posed problem.
</blockquote>

<LI> <B><A NAME="rvs95-seitz">
     Physically-Valid View Synthesis by Image Interpolation</A></B><BR>
     S. M. Seitz and C. R. Dyer, <CITE>Proc. Workshop on Representation
     of Visual Scenes</CITE>, 1995, 18-25.
     (<!WA68><!WA68><!WA68><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/rvs95-seitz.ps">postscript</A>
     or <!WA69><!WA69><!WA69><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/rvs95-seitz.ps.gz">500K gzip'ed postscript</A>)<P>
<blockquote>
Image warping is a popular tool for
smoothly transforming one image to another.  ``Morphing''
techniques based on geometric image interpolation create compelling visual
effects, but the validity of such transformations has not been established.
In particular, does 2D interpolation of two
views of the same scene produce a sequence of physically valid in-between
views of that scene?  In this paper, we describe a simple image rectification
procedure which guarantees that interpolation does in fact produce valid views,
under generic assumptions about visibility and the projection process.
Towards this end, it is first shown that two basis views are sufficient to
predict the appearance of the scene within a specific range of new viewpoints.
Second, it is demonstrated that interpolation of the rectified basis images
produces exactly this range of views.
Finally, it is shown that generating this range of views is a theoretically
well-posed problem, requiring neither knowledge of camera positions nor
3D scene reconstruction.
A scanline algorithm for view interpolation is presented that requires only
four user-provided feature correspondences to produce valid orthographic
views.  The quality of the resulting images is demonstrated with
interpolations of real imagery.
</blockquote>


<LI> <B><A NAME="pami93-eggert">
     The Scale Space Aspect Graph</A></B><BR>
     D. W. Eggert, K. W. Bowyer, C. R. Dyer, H. I. Christensen
     and D. B. Goldgof, <CITE>IEEE Trans. Pattern Analysis and
     Machine Intelligence</CITE><B> 15</B>, 1993, 1114-1130.
     (<!WA70><!WA70><!WA70><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/pami93-eggert.ps">postscript</A>
     or <!WA71><!WA71><!WA71><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/pami93-eggert.ps.gz">280K gzip'ed postscript</A>)<BR>
     (An earlier
     version of this paper appeared in
     <CITE>Proc. Computer Vision and Pattern Recognition Conf.</CITE>,
     1992, 335-340
     (<!WA72><!WA72><!WA72><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/cvpr92-eggert.ps">postscript</A>
     or <!WA73><!WA73><!WA73><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/cvpr92-eggert.ps.gz">250K gzip'ed postscript</A>).)
     <P> 
<blockquote>
Currently the aspect graph is computed from the theoretical standpoint 
of perfect resolution in object shape, the viewpoint and the projected image.
This means that the aspect graph may include details that an observer could 
never see in practice. Introducing the notion of scale into the aspect graph 
framework provides a mechanism for selecting a level of detail that is 
"large enough" to merit explicit representation. This effectively allows 
control over the number of nodes retained in the aspect graph. This paper 
introduces the concept of the scale space aspect graph, defines three 
different interpretations of the scale dimension, and presents a detailed 
example for a simple class of objects, with scale defined in terms of the 
spatial extent of features in the image.
</blockquote>


<LI> <B><A NAME="cvgip92-seales">
     Viewpoint from Occluding Contour</A></B><BR>
     W. B. Seales and C. R. Dyer, 
     <CITE>Computer Vision, Graphics and Image Processing:  Image
     Understanding</CITE><B> 55</B>, 1992, 198-211.
     (<!WA74><!WA74><!WA74><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/cvgip92-seales.ps">postscript</A>
     or <!WA75><!WA75><!WA75><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/cvgip92-seales.ps.gz">290K gzip'ed postscript</A>)<P>
<blockquote>
In this paper we present the geometry and the algorithms for organizing a
viewer-centered representation of the occluding contour of polyhedra.
The contour is computed from a polyhedral boundary model as it would appear
under orthographic projection into the image plane from every viewpoint
on the view sphere.
Using this representation, we show how to derive constraints on regions in
viewpoint space from the relationship between detected image features and
our precomputed contour model.
Such constraints are based on both qualitative (viewpoint extent) and
quantitative (angle measurements and relative geometry) information that has
been precomputed about how the contour appears in the image plane as a set
of projected curves and T-junctions from self-occlusion.
The results we show from an experimental system demonstrate that features
of the occluding contour can be computed in a model-based framework, and
and their geometry constrains the viewpoints from which a model will project
to a set of occluding contour features in an image.
</blockquote>


<LI> <B><A NAME="ecai92-seales">
     An Occlusion-Based Representation of Shape for 
     Viewpoint Recovery</A></B><BR>
     W. B. Seales and C. R. Dyer, 
     <CITE>Proc. 10th European Conf. on Artificial Intelligence</CITE>,
     1992, 816-820.
     (<!WA76><!WA76><!WA76><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/ecai92-seales.ps">postscript</A>
     or <!WA77><!WA77><!WA77><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/ecai92-seales.ps.gz">80K gzip'ed postscript</A>)<P>
<blockquote>
In this paper we present the geometry and the algorithms for organizing and
using a viewer-centered representation of the occluding contour of polyhedra.
The representation is computed from a polyhedral model
under orthographic projection for all viewing directions.
Using this representation, we derive constraints on
viewpoint correspondences between image features and
model contours.
Our results show that the occluding contour, computed
in a model-based framework, can be used to strongly constrain the viewpoints
where a 3D model matches the occluding contour features of the image.
</blockquote>


<LI> <B><A NAME="thesis-seales">
     Appearance Models of Three-Dimensional 
     Shape for Machine Vision and Graphics</A></B><BR>
     Ph.D. Dissertation, W. B. Seales,
     Computer Sciences Department Technical Report 1042,
     August 1991.
     (<!WA78><!WA78><!WA78><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/thesis-seales.ps">postscript</A>
     or <!WA79><!WA79><!WA79><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/thesis-seales.ps.gz">460K gzip'ed postscript</A>)<P>
<blockquote>
A fundamental problem common to both computer graphics and model-based
computer vision is how to efficiently model the appearance of a shape.
Appearance is obtained procedurally by applying a projective transformation
to a three-dimensional object-centered shape representation.
This thesis presents a viewer-centered representation that is based on the
visual event, a viewpoint where a specific change in the structure of the
projected model occurs.
We present and analyze the basis of this viewer-centered representation
and the algorithms for its construction.
Variations of this visual-event-based representation are applied to two
specific problems:  hidden line/surface display, and the solution for model
pose given an image contour.
<P>

The problem of how to efficiently display a polyhedral scene over a path
of viewpoints is cast as a problem of computing visual events along that path.
A visual event is a viewpoint that causes a change in the structure of
the image structure graph, a model's projected line drawing.
The information stored with a visual event is sufficient to update
a representation of the image structure graph.
Thus the visible lines of a scene can be displayed as viewpoint changes
by first precomputing and storing visual events, and then using those events
at display time to interactively update the image structure graph.
Display rates comparable to wire-frame display are achieved for large
polyhedral models.
<P>

The rim appearance representation is a new, viewer-centered, exact
representation of the occluding contour of polyhedra.
We present an algorithm based on the geometry of polyhedral self-occlusion
and on visual events for computing a representation of the exact appearance
of occluding contour edges.
The rim appearance representation, organized as a multi-level model of the
occluding contour, is used to constrain the viewpoints of
a three-dimensional model that can produce a set of detected
occluding-contour features.
Implementation results demonstrate that precomputed occluding-contour
information efficiently and tightly constrains the pose of a model while
consistently accounting for detected occluding-contour features.
</blockquote>


</UL>
<HR>
<P>
<H2><A NAME="snakes">Deformable Contours</A></H2>
<UL>

<LI><B><A NAME="pami94-lai">
     Deformable Contours: Modeling and Extraction</A></B><BR>
     K. F. Lai and R. T. Chin,
     <CITE>IEEE Trans. Pattern Analysis and Machine Intell.</CITE> <B>17</B>,
     1995, 1084-1090.  
     (<!WA80><!WA80><!WA80><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/pami94-lai.ps">postscript</A>
     or <!WA81><!WA81><!WA81><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/pami94-lai.ps.gz">350K gzip'ed postscript</A>)<BR>
     (An earlier version appeared in
     <CITE>Proc. Computer Vision and Pattern Recognition Conf.</CITE>,
     1994, 601-608
     (<!WA82><!WA82><!WA82><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/cvpr94-lai.ps">postscript</A>
     or <!WA83><!WA83><!WA83><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/cvpr94-lai.ps.gz">220K gzip'ed postscript</A>).)
<P>
<blockquote>
This paper considers the problem of modeling and extracting arbitrary deformable 
contours from noisy images. We propose a global contour model based on a stable 
and regenerative shape matrix, which is invariant and unique under rigid 
motions. Combined with Markov random field to model local deformations, this 
yields prior distribution that exerts influence over a global model while 
allowing for deformations. We then cast the problem of extraction into posterior 
estimation and show its equivalence to energy minimization of a generalized 
active contour model. We discuss pertinent issues in shape training, energy 
minimization, line search strategies, minimax regularization and initialization 
by generalized Hough transform. Finally, we present experimental results and 
compare its performance to rigid template matching.
</blockquote>


<LI> <B><A NAME="icarcv94-lai">
     On Classifying Deformable Contours Using the Generalized
     Active Contour Model</A></B><BR>
     K. F. Lai and R. T. Chin,
     <CITE>Proc. Int. Conf. Automation, Robotics and Computer Vision</CITE>,  
     Singapore, 1994.  
     (<!WA84><!WA84><!WA84><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/icarcv94-lai.ps">postscript</A>
     or <!WA85><!WA85><!WA85><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/icarcv94-lai.ps.gz">150K gzip'ed postscript</A>)<P>
<blockquote>
Recently, we proposed the generalized active contour model (g-snake) to model 
and extract deformable contours from noisy images. This paper demonstrates the 
usefulness of g-snake in classifying among several candidate deformable 
contours. The g-snake is suitable for this task because its shape 
representation is unique, affine invariant and possesses
metric properties. We derive the 
optimal classification test and show that this requires marginalization of the 
distribution. However, as the summation is peaked around the posterior estimate 
in most practical applications, only small regions need to be considered.  
Finally, we performed extensive experimentations and report significant 
improvement over matched template in handwritten numeral recognition.
</blockquote>


<LI> <B><A NAME="thesis-lai">
     Deformable Contours: Modeling, Extraction,
     Detection and Classification</A></B><BR>
     Ph.D. Dissertation, K. F. Lai,
     Electrical and Computer Engineering Department,
     August 1994.
     (<!WA86><!WA86><!WA86><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/thesis-lai.ps">postscript</A>
     or <!WA87><!WA87><!WA87><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/thesis-lai.ps.gz">820K gzip'ed postscript</A>)<P>
<blockquote>
This thesis presents an integrated approach in modeling, extracting, detecting 
and classifying deformable contours directly from noisy images. We begin by 
conducting a case study on regularization, formulation and initialization of
the active contour models (snakes). Using minimax principle, we derive a 
regularization criterion whereby the values can be automatically and implicitly 
determined along the contour. Furthermore, we formulate a set of energy 
functionals which yield snakes that contain Hough transform as a special case. 
Subsequently, we consider the problem of modeling and extracting arbitrary 
deformable contours from noisy images. We combine a stable, invariant and
unique contour model with Markov random field to yield prior
distribution that exerts 
influence over an arbitrary global model while allowing for deformation. Under 
the Bayesian framework, contour extraction turns into posterior estimation, 
which is in turn equivalent to energy minimization in a generalized active 
contour model. Finally, we integrate these lower level visual tasks with
pattern recognition processes of detection and classification. Based on the 
Nearman-Pearson lemma, we derive the optimal detection and classification
tests.  As the summation is peaked in most practical applications,
only small regions 
need to be considered in marginalizing the distribution. The validity of our 
formulation have been confirmed by extensive and rigorous experimentations.
</blockquote>


<LI> <B><A NAME="accv93-lai">
     On Regularization, Formulation and Initialization of
     Active Contour Models (Snakes)</A></B><BR>
     K. F. Lai and R. T. Chin,
     <CITE>Proc. 1st Asian Conf. on Computer Vision</CITE>,  
     1993, 542-545.  
     (<!WA88><!WA88><!WA88><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/accv93-lai.ps">postscript</A>
     or <!WA89><!WA89><!WA89><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/accv93-lai.ps.gz">150K gzip'ed postscript</A>)<P>
<blockquote>
In snake formulation, large regularization enhances the robustness against noise 
and incomplete data, while small values increase the accuracy in capturing 
boundary variations. We present a local minimax criterion which automatically 
determines the optimal regularization at every locations along the boundary with 
no added computation cost. We also modify existing energy formulations to repair 
deficiencies in internal energy and improve performance in external energy. This 
yields snakes that contain Hough transform as a special case. We can therefore 
initialize the snake efficiently and reliably using Hough transform.
</blockquote>
</UL>
<HR>


<P>
<H2><A NAME="visualization">Visualization</A></H2>
<UL>

<LI><B><A NAME="thesis-hibbard">
     Visualizing Scientific Computations: A System based on
     Lattice-Structured Data and Display Models</A></B><BR>
     W. L. Hibbard, Ph.D. Dissertation,
     Computer Sciences Department Technical Report 1226,
     University of Wisconsin-Madison, 1995.
     (<!WA90><!WA90><!WA90><A HREF="ftp://iris.ssec.wisc.edu/pub/lattice">600K compress'ed postscript</A>)<P>
<blockquote>
In this thesis we develop a system that makes scientific
computations visible and enables physical scientists to perform visual
experiments with their computations.  Our approach is unique in the way
it integrates visualization with a scientific programming language.  Data
objects of any user-defined data type can be displayed, and can be
displayed in any way that satisfies broad analytic conditions, without
requiring graphics expertise from the user.  Furthermore, the system is
highly interactive.
<P>
In order to achieve generality in our architecture, we first analyze
the nature of scientific data and displays, and the visualization mappings
between them.  Scientific data and displays are usually approximations to
mathematical objects (i.e., variables, vectors and functions) and this
provides a natural way to define a mathematical lattice structure on data
models and display models.  Lattice-structured models provide a basis for
integrating certain forms of scientific metadata into the computational and
display semantics of data, and also provide a rigorous interpretation of
certain expressiveness conditions on the visualization mapping from data
to displays.  Visualization mappings satisfying these expressiveness
conditions are lattice isomorphisms.  Applied to the data types of a
scientific programming language, this implies that visualization mappings
from data aggregates to display aggregates can always be decomposed
into mappings of data primitives to display primitives.
<P>
These results provide very flexible data and display models, and
provide the basis for flexible and easy-to-use visualization of data objects
occurring in scientific computations.
</blockquote>


<LI> <B><A NAME="computer94-hibbard">
     Interactive Visualization of Earth and Space Science Computations</A></B><BR>
     W. L. Hibbard, B. E. Paul, A. L. Battaiola, D. A. Santek,
     M-F. Voidrot-Martinez, and C. R. Dyer,
     <CITE>Computer</CITE><B> 27</B>, No. 7, July 1994, 65-72.
     (<!WA91><!WA91><!WA91><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/computer94-hibbard.ps">postscript</A>
     or <!WA92><!WA92><!WA92><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/computer94-hibbard.ps.gz">20K gzip'ed postscript</A>)<P>
<blockquote>
We describe techniques that enable Earth and space scientists
to interactively visualize and experiment with their computations.
Numerical simulations of the Earth's atmosphere and oceans generate
large and complex data sets, which we visualize in a highly interactive
virtual Earth environment.  We use data compression and distributed
computing to maximize the size of simulations that can be explored,
and a user interface tuned to the needs of environmental modelers.
For the broader class of computations used by scientists we have
developed more general techniques, integrating visualization with an
environment for developing and executing algorithms.  The key is
providing a flexible data model that lets users define data types
appropriate for their algorithms, and also providing a display model
that lets users visualize those data types without placing a substantial
burden of graphics knowledge on them.
</blockquote>


<LI> <B><A NAME="vis94-hibbard">
     A Lattice Model for Data Display</A></B><BR>
     W. L. Hibbard, C. R. Dyer, and B. E. Paul,
     <CITE>Proc. Visualization '94</CITE>, 1994, 310-317.
     (<!WA93><!WA93><!WA93><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/vis94-hibbard.ps">postscript</A>
     or <!WA94><!WA94><!WA94><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/vis94-hibbard.ps.gz">60K gzip'ed postscript</A>)<P>
<blockquote>
In order to develop a foundation for visualization, we develop
lattice models for data objects and displays that focus on the fact that
data objects are approximations to mathematical objects and real
displays are approximations to ideal displays.  These lattice models
give us a way to quantize the information content of data and displays
and to define conditions on the visualization mappings from data to
displays.  Mappings satisfy these conditions if and only if they are
lattice isomorphisms.  We show how to apply this result to scientific
data and display models, and discuss how it might be applied to
recursively defined data types appropriate for complex information
processing.
</blockquote>


<LI> <B><A NAME="vis92-hibbard">
     Display of Scientific Data Structures for Algorithm Visualization</A></B><BR>
     W. Hibbard, C. R. Dyer, and B. Paul,
     <CITE>Proc. Visualization '92</CITE>, 1992, 139-146.
     (<!WA95><!WA95><!WA95><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/vis92-hibbard.ps">postscript</A>
     or <!WA96><!WA96><!WA96><A HREF="ftp://ftp.cs.wisc.edu/computer-vision/vis92-hibbard.ps.gz">60K gzip'ed postscript</A>)<P>
<blockquote>
We present a technique for defining graphical depictions for all
the data types defined in an algorithm.  The ability to display arbitrary
combinations of an algorithm's data objects in a common frame of
reference, coupled with interactive control of algorithm execution,
provides a powerful way to understand algorithm behavior.  Type
definitions are constrained so that all primitive values occurring in data
objects are assigned scalar types.  A graphical display, including user
interaction with the display, is modeled by a special data type.
Mappings from the scalar types into the display model type provide a
simple user interface for controlling how all data types are depicted,
without the need for type-specific graphics logic.
</blockquote>

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